Instability of the finite-difference split-step method applied to the nonlinear Schrödinger equation. I. standing soliton

Taras I. Lakoba

doi:10.1002/num.22040

Instability of the finite-difference split-step method applied to the nonlinear Schrödinger equation. I. standing soliton

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22040 ◽

2015 ◽

Vol 32 (3) ◽

pp. 1002-1023 ◽

Cited By ~ 1

Author(s):

Taras I. Lakoba

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Step Method ◽

Nonlinear Schrödinger

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Instability of the finite-difference split-step method applied to the nonlinear Schrödinger equation. II. moving soliton

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22039 ◽

2015 ◽

Vol 32 (3) ◽

pp. 1024-1040 ◽

Cited By ~ 3

Author(s):

Taras I. Lakoba

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Step Method ◽

Nonlinear Schrödinger

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Instability of the finite-difference split-step method applied to the generalized nonlinear Schrödinger equation. III. external potential and oscillating pulse solutions

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22071 ◽

2016 ◽

Vol 33 (3) ◽

pp. 633-650 ◽

Cited By ~ 1

Author(s):

Taras I. Lakoba

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

External Potential ◽

Step Method ◽

Nonlinear Schrödinger ◽

Generalized Nonlinear Schrödinger Equation

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On the conservative finite difference scheme for 2D nonlinear Schrödinger equation

Computer Physics Communications ◽

10.1016/s0010-4655(06)70082-0 ◽

1999 ◽

Vol 121-122 ◽

pp. 677

Author(s):

Yu.F. Kir'yanov ◽

M.L. Kudryavtseva ◽

M.V. Maslov ◽

I.V. Shestakova

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Difference Scheme ◽

Nonlinear Schrödinger Equation ◽

Finite Difference Scheme ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Conservative Finite Difference Scheme

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A comparative numerical study based on cubic exponential B-splines and finite difference method for the nonlinear Schrödinger equation

10.1063/1.5136440 ◽

2019 ◽

Author(s):

Azhar Ahmad ◽

Amirah Azmi ◽

Nur Nadiah Abd Hamid ◽

Ahmad Izani Md. Ismail

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Difference Method ◽

Schrodinger Equation ◽

Numerical Study ◽

Nonlinear Schrodinger Equation ◽

B Splines ◽

Nonlinear Schrödinger

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Finite difference solutions of the nonlinear Schrödinger equation and their conservation of physical quantities

Communications in Mathematical Sciences ◽

10.4310/cms.2007.v5.n4.a2 ◽

2007 ◽

Vol 5 (4) ◽

pp. 779-788 ◽

Cited By ~ 4

Author(s):

Clemens Heitzinger ◽

Christian Ringhofer ◽

Siegfried Selberherr

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Physical Quantities

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Finite difference method with cubic spline for solving nonlinear schrödinger equation

International Journal of Computer Mathematics ◽

10.1080/00207169608804528 ◽

1996 ◽

Vol 62 (1-2) ◽

pp. 101-112 ◽

Cited By ~ 9

Author(s):

M. S. Ismail

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Difference Method ◽

Schrodinger Equation ◽

Cubic Spline ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Unconditional $$L^{\infty }$$ L ∞ -convergence of two compact conservative finite difference schemes for the nonlinear Schrödinger equation in multi-dimensions

CALCOLO ◽

10.1007/s10092-018-0277-0 ◽

2018 ◽

Vol 55 (3) ◽

Cited By ~ 2

Author(s):

Tingchun Wang ◽

Xiaofei Zhao

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Difference Schemes ◽

Finite Difference Schemes ◽

Nonlinear Schrödinger

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A Linear Finite Difference Scheme for the Two-Dimensional Nonlinear Schrödinger Equation with Fractional Laplacian

Journal of Scientific Computing ◽

10.1007/s10915-021-01703-9 ◽

2021 ◽

Vol 90 (1) ◽

Author(s):

Yanyan Wang ◽

Zhaopeng Hao ◽

Rui Du

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Difference Scheme ◽

Nonlinear Schrödinger Equation ◽

Finite Difference Scheme ◽

Schrodinger Equation ◽

Fractional Laplacian ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger

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Highly accurate finite difference method for coupled nonlinear Schrödinger equation

International Journal of Computer Mathematics ◽

10.1080/00207160410001661339 ◽

2004 ◽

Vol 81 (3) ◽

pp. 333-351 ◽

Cited By ~ 48

Author(s):

M. S. Ismail ◽

S. Z. Alamri

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Difference Method ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Coupled Nonlinear Schrödinger Equation

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Nonstandard finite difference variational integrators for nonlinear Schrödinger equation with variable coefficients

Advances in Difference Equations ◽

10.1186/1687-1847-2013-12 ◽

2013 ◽

Vol 2013 (1) ◽

Cited By ~ 9

Author(s):

Cuicui Liao ◽

Xiaohua Ding

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Variable Coefficients ◽

Nonlinear Schrodinger Equation ◽

Variational Integrators ◽

Nonlinear Schrödinger ◽

Nonstandard Finite Difference

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